Would severe heat distort/bow the barrel?
Severe heat could, it could also melt it, but the more insidious damage comes from removing the temper from steel. In an insulated environment, if the steel has gotten hot enough (above its crystallization temperature) and cools slowly, it will lose temper and soften.

In this instance, though, we have a thermometer.
Consider, according to
https://concealednation.org/2016/06/ammo-in-the-car-under-summer-heat-how-stable-is-it/ Lead melts at 621 °F
Nitrocellulose ignites at around 320-338 °F
Gunpowder ignites at 801–867 °F.
Ordinary book paper ignites at 451°F (Hence the Ray Bradbury Title), and most paper would be burning by 500°F
While the 7mm ammo cooked off (nitrocellulose based powder?), the pistol ammo did not, and the boxes were not carbonized. That means temperatures likely stayed below 500 degrees F, and the steel is okay.
Still, after I cleaned the rifles and pistol up, I would take them to a gunsmith or metallurgist and have the actions hardness tested to be sure.